Automatic Response Category Combination in Multinomial Logistic Regression

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9 Scopus citations


We propose a penalized likelihood method that simultaneously fits the multinomial logistic regression model and combines subsets of the response categories. The penalty is nondifferentiable when pairs of columns in the optimization variable are equal. This encourages pairwise equality of these columns in the estimator, which corresponds to response category combination. We use an alternating direction method of multipliers algorithm to compute the estimator and we discuss the algorithm’s convergence. Prediction and model selection are also addressed. Supplemental materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)758-766
Number of pages9
JournalJournal of Computational and Graphical Statistics
Issue number3
StatePublished - Jul 3 2019

Bibliographical note

Funding Information:
This research is partially supported by the National Science Foundation grant DMS-1452068. The authors thank the referees and the associate editor for helpful comments.

Publisher Copyright:
© 2019, © 2019 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.


  • Fusion penalty
  • Multinomial logistic regression
  • Response category reduction


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